A reliability-based method for optimization programming problems

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Abstract

In this study, a method is developed to solve general
stochastic programming problems. The method is applicable to
both linear and nonlinear optimization. Based on a proper
linearization, a set of probabilistic constraints (performance
functions) can be transformed into a corresponding set of
deterministic constraints. this is accomplish by expanding all
the constraints about the most probable failure point. The use
of the proposed method allows the simplification of any
stochastic programming problems into a standard linear
programming problem. Numerical examples are applied to the
area of probability- based optimum structural design.